{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/weisfeiler-and-leman-go-infinite-spectral-and","title":"Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings","arxiv_id":"2201.13410","date":"2022-01-31","proceeding":null,"authors":["Or Feldman","Amit Boyarski","Shai Feldman","Dani Kogan","Avi Mendelson","Chaim Baskin"],"abstract":"Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the Weisfeiler-Leman (WL) test) and spectral invariants. While the exact power of the latter is still an open question, the former is regularly criticized for its limited power, when a standard configuration of uniform pre-coloring is used. This drawback hinders the applicability of Message Passing Graph Neural Networks (MPGNNs), whose expressive power is upper bounded by the WL test. Relaxing the assumption of uniform pre-coloring, we show that one can increase the expressive power of the WL test ad infinitum. Following that, we propose an efficient pre-coloring based on spectral features that provably increase the expressive power of the vanilla WL test. The above claims are accompanied by extensive synthetic and real data experiments. The code to reproduce our experiments is available at https://github.com/TPFI22/Spectral-and-Combinatorial","url_abs":"https://arxiv.org/abs/2201.13410v2","url_pdf":"https://arxiv.org/pdf/2201.13410v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"weisfeiler-and-leman-go-infinite-spectral-and","repo_url":"https://github.com/tpfi22/spectral-and-combinatorial","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"isomorphism-testing","task_name":"Isomorphism Testing"},{"task_slug":"open-question","task_name":"Open-Ended Question Answering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/2201.13410","atlas_url":"https://app.syntology.ai/?focus=2201.13410","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2201.13410"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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